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# If Mars is about 10% of Earth mass why it has 38% gravity of Earth?

Trying to understand.

### 9 Answers

- 1 month agoFavorite Answer
The equation to use is F = G(m1)(m2)/r^2.

If m1 is the mass of the planet, and r is it's radius, then you can see that the as the radius gets big, the force of gravity (F) drops very quick. But, as the radius gets small, then F gets quite large.

So, let's say you weigh 100N on Earth.

100N = G(m1)(m2)/r^2, where G is the gravitational constant, m1 is the mass of Earth (let's call it "1") and r is the radius of Earth (We'll call that "1" also)...

100N = G(1)(m2)/1 Since G and m2 are the same (m2 is your mass), we'll make that a constant called W

100N = W(1)/1 = W = 100

Now on Mars, it's radius is 3,389 km, and Earth's is 6,371; so Mars has only 53% of our radius...

F = G(0.10)(m2)/(0.53)^2

F = W(0.10) / 0.289

F = W(.356)

F = 35.6N on Mars.

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- oyubirLv 61 month ago
And 53% of its radius.

Gravity at the surface of a planet is proportional to the mass of the planet, and inversely proportional to the square of the radius of the planet.

10% / 53%² = 0.10 / 0.53² = 36%.

(38% if you use the more accurate value 10.7% for mass)

(Roughly speaking, 10 times less mass, for 2 times less radius ⇒ 10 times less gravity because of the mass, but 4 (2²) times MORE gravity because of the radius. So, around 40% of the gravity all together)

- Anonymous1 month ago
It has magnets under the surface.

- billrussell42Lv 71 month ago
mass is not the only factor. a planet could have the mass of earth, and twice the radius, and it would have 1/4 the gravity. Or, 1/2 the radius and 4 times the gravity.

or a planet with the same radius and half the mass would have g of 1/2.

for mars, M = 6.42e23 kg, R = 3.39e6 m

g = (6.674e-11)(6.42e23) / (3.39e6)² = 3.73 m/s²

the exact equation is:

g = GM/R²

where

G = 6.674e-11 m³/kgs²

M is mass of planet

R is radius

Gravitational attraction in newtons

F = G m₁m₂/r²

G = 6.674e-11 m³/kgs²

m₁ and m₂ are the masses of the two objects in kg

r is the distance in meters between their centers

- nebLv 71 month ago
I have no idea whether your numbers are correct or not, but remember mars is smaller so it is a shorter distance from the surface to the center of the planet. Remember you can think of all of the mass being at the center, and the strength of gravity at the surface depends on both mass AND radius (distance from center) of the planet.